Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class A {


	public static void main(String[] args) throws Exception{

		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int n = sc.nextInt();
		int m = sc.nextInt();
		
		int[][] g = new int[n][m];
		
		for (int i = 0; i < n; i++) 
			for (int j = 0; j < m; j++)
				g[i][j] = sc.nextInt();
		
		int[] col = new int[m]; int[] row = new int[n];
		int min = (int) 1e9;
		for (int c = 0; c <= g[0][0]; c++) {
			int r = g[0][0] - c;
			
			int[] colT = new int[m];
			int[] rowT = new int[n];
			
			boolean can = true;
			int count = 0;
			
			for (int i = 0; i < n && can; i++) {
				if(g[i][0] < c)
					can = false;
				else {
					rowT[i] = g[i][0] - c;
					count += rowT[i];
				}
			}
			
			for (int i = 0; i < m && can; i++) {
				if(g[0][i] < r)
					can = false;
				else {
					colT[i] = g[0][i] - r;
					count += colT[i];
				}
			}
			
			for (int i = 0; i < n && can; i++) {
				for (int j = 0; j < m && can; j++) {
					if(g[i][j] != rowT[i] + colT[j])
						can = false;
				}
			}
			
			if(can && count <= min) {
				min = count;
				col = colT; row = rowT;
			}
		}
		
		if(min < 1e9) {
			out.println(min);
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < row[i]; j++) 
					out.println("row " + (i + 1));
			}
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < col[i]; j++) 
					out.println("col " + (i + 1));
			}
		}else
			out.println(-1);
				
			

		out.flush();
	}

	

	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream System){br = new BufferedReader(new InputStreamReader(System));}
		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public String nextLine()throws IOException{return br.readLine();}
		public int nextInt() throws IOException {return Integer.parseInt(next());}
		public double nextDouble() throws IOException {return Double.parseDouble(next());}
		public char nextChar()throws IOException{return next().charAt(0);}
		public Long nextLong()throws IOException{return Long.parseLong(next());}
		public boolean ready() throws IOException{return br.ready();}
		public void waitForInput(){for(long i = 0; i < 3e9; i++);}
	}
}